scholarly journals On the two-times differentiability of the value functions in the problem of optimal investment in incomplete markets

2006 ◽  
Vol 16 (3) ◽  
pp. 1352-1384 ◽  
Author(s):  
Dmitry Kramkov ◽  
Mihai Sîrbu
Keyword(s):  
Incomplete Markets ◽  
Optimal Investment ◽  
Value Functions

On the properties of dynamic value functions in the problem of optimal investment in incomplete markets

2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Michael Mania ◽  
Revaz Tevzadze
Keyword(s):  
Incomplete Markets ◽  
Real Line ◽  
Value Function ◽  
Optimal Solution ◽  
Optimal Investment ◽  
Maximization Problem ◽  
Value Functions ◽  
Utility Maximization Problem ◽  
The Value Function ◽  
Uniformly Bounded

AbstractWe study the analytical properties of a dynamic value function and of an optimal solution to the utility maximization problem in incomplete markets for utility functions defined on the whole real line. It was shown by Kramkov and Sirbu [Ann. Appl. Probab. 16 (2006), no. 3, 1352–1384] that if the relative risk-aversion coefficient of the utility function defined on the half real line is uniformly bounded away from zero and infinity, then the value function at time

scholarly journals On Market Completions Approach to Option Pricing

2021 ◽  
Vol 9 (3) ◽  
pp. 77-93
Author(s):  
I. Vasilev ◽  
A. Melnikov
Keyword(s):  
Option Pricing ◽  
Incomplete Markets ◽  
Option Price ◽  
Optimal Investment ◽  
Market Model ◽  
Option Prices ◽  
End Points ◽  
Hedging Strategies ◽  
Risk Neutral ◽  
Interesting Approach

Option pricing is one of the most important problems of contemporary quantitative finance. It can be solved in complete markets with non-arbitrage option price being uniquely determined via averaging with respect to a unique risk-neutral measure. In incomplete markets, an adequate option pricing is achieved by determining an interval of non-arbitrage option prices as a region of negotiation between seller and buyer of the option. End points of this interval characterise the minimum and maximum average of discounted pay-off function over the set of equivalent risk-neutral measures. By estimating these end points, one constructs super hedging strategies providing a risk-management in such contracts. The current paper analyses an interesting approach to this pricing problem, which consists of introducing the necessary amount of auxiliary assets such that the market becomes complete with option price uniquely determined. One can estimate the interval of non-arbitrage prices by taking minimal and maximal price values from various numbers calculated with the help of different completions. It is a dual characterisation of option prices in incomplete markets, and it is described here in detail for the multivariate diffusion market model. Besides that, the paper discusses how this method can be exploited in optimal investment and partial hedging problems.

Portfolio Optimization in Incomplete Markets

2019 ◽  
pp. 426-435
Author(s):  
Tomas Björk
Keyword(s):  
Portfolio Optimization ◽  
Incomplete Markets ◽  
Duality Theory ◽  
Optimal Investment ◽  
Optimal Consumption ◽  
Finite Sample ◽  
Martingale Approach ◽  
Dual Approach ◽  
Full Theory ◽  
Optimal Investment Problem

The object of this chapter is to give an overview of the dual approach to portfolio optimization in incomplete markets. The main result of this theory is that to every optimal investment problem there is a dual problem where we minimize a dual objective function over the class of martingale measures. For the case of a finite sample space we can present the full theory, but for the general case we only outline the proof. The theory is closely connected to convex duality theory and to the martingale approach to optimal consumption/investment discussed in Chapter 27.

scholarly journals Optimal investment with intermediate consumption under no unbounded profit with bounded risk

2017 ◽  
Vol 54 (3) ◽  
pp. 710-719 ◽  
Author(s):  
Huy N. Chau ◽  
Andrea Cosso ◽  
Claudio Fontana ◽  
Oleksii Mostovyi
Keyword(s):  
Utility Maximization ◽  
Optimal Investment ◽  
Incomplete Market ◽  
Value Functions ◽  
Stochastic Field ◽  
Intermediate Consumption ◽  
Bounded Risk ◽  
Primal And Dual

Abstract We consider the problem of optimal investment with intermediate consumption in a general semimartingale model of an incomplete market, with preferences being represented by a utility stochastic field. We show that the key conclusions of the utility maximization theory hold under the assumptions of no unbounded profit with bounded risk and of the finiteness of both primal and dual value functions.

scholarly journals Optimal investment with random endowments in incomplete markets

2004 ◽  
Vol 14 (2) ◽  
pp. 845-864 ◽  
Author(s):  
Julien Hugonnier ◽  
Dmitry Kramkov
Keyword(s):  
Incomplete Markets ◽  
Optimal Investment

scholarly journals Optimal investment-reinsurance strategy in the correlated insurance and financial markets

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Xiaoyu Xing ◽  
Caixia Geng
Keyword(s):  
Financial Markets ◽  
Asset Allocation ◽  
Value Function ◽  
Optimal Investment ◽  
Value Functions ◽  
Cev Model ◽  
Surplus Process ◽  
Novel Approach ◽  
Exponential Utility Function ◽  
Allocation Strategies

<p style='text-indent:20px;'>Within the correlated insurance and financial markets, we consider the optimal reinsurance and asset allocation strategies. In this paper, the risk asset is assumed to follow a general continuous diffusion process driven by a Brownian motion, which correlates to the insurer's surplus process. We propose a novel approach to derive the optimal investment-reinsurance strategy and value function for an exponential utility function. To illustrate this, we show how to derive the explicit closed strategies and value functions when the risk asset is the CEV model, 3/2 model and Merton's IR model respectively.</p>

Sign in / Sign up

Export Citation Format

Share Document